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Natural connections on the bundle of Riemannian metrics

Roberto Ferreiro Perez·Jaime Muñoz Masque
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Abstract

Let $FM,\mathcal{M}_M$ be the bundles of linear frames and Riemannian metrics of a manifold $M$, respectively. The existence of a unique $\mathrm{Diff}M$-invariant connection form on $J^1\mathcal{M}_M\times_MFM\to J^1\mathcal{M}_M$, which is Riemannian with respect to the universal metric on $J^1\mathcal{M}_M\times_MTM$, is proved. Aplications to the construction of universal Pontryagin and Euler forms, are given.

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Roberto Ferreiro Perez, Jaime Muñoz Masque. 2005-07-04. Natural connections on the bundle of Riemannian metrics. https://arxiv.org/abs/math/0507075

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